### Angular Displacement

**Purpose:**
- To show that one cannot regard finite angular displacement as a vector quantity because the additions of such rotations do not obey the commutative law.

**Equipment:**
- Large textbook, large wooden dice.

**Procedure:**
- Choose two rotations for the textbook. Call these rotations
*O1* and *O2* respectively. Performing the rotations, show that *O1* + *O2* does not equal *O2* + *O1*. In such cases, the final positions of the book are quite different. It should be mentioned that infinitesimal angular displacements do add commutatively, hence angular velocities and accelerations do behave like vectors. The large pair of dice may also be used to illustrate this principle.